Dear Melissa,
Thank you for writing to T2T. It looks like your math department has come
across one of the "small drawbacks" for using acronyms like PEMDAS (or
BEDMAS) for the order of operations. The acronyms are intended to help
students (and for the most part do so) to remember that they must compute
operations that are in parentheses (or brackets) first, then exponents, and
then multiplication/division, then addition/subtraction.
The drawback is that there is no way that the acronym can explain that
multiplication and division are "equal in stature" when it comes to which one
is performed first--SO mathematical convention agrees that you will do
multiplications/divisions as they occur "from left to right". Similarly,
addition and subtraction are "equal in stature" in the order of operations,
so they, too (after everything else is computed) would be done as they
occur "from left to right."
In your example, since (5-3) is in parentheses, it would be done first--
since it is then raised to the exponent 2, that would be done next, so you
would have at this point 75 + 36 (divided by) 3 (times) 4. You would then do
the divisions and multiplications as they occur from left to right, so you
would have 75 + 12 X 4 , or 75 + 48, or 123. You'll notice that "PEMDAS"
gives the "impression" that you'd do multiplication before division, while
"BEDMAS" gives the "impression" that you'd do division before multiplication.
Sorry for the long-winded explanation--hope it made some sense.
-Ralph, for the T2T service